Environ Resource Econ (2016) 63:505–522DOI 10.1007/s10640-014-9836-2

Moral Behaviour, Altruism and Environmental Policy

Marc Daube · David Ulph

Accepted: 26 September 2014 / Published online: 16 October 2014© The Author(s) 2014. This article is published with open access at Springerlink.com

Abstract Free-riding is often associated with self-interested behaviour. However, if thereis a global pollutant, free-riding will arise if individuals calculate that their emissions arenegligible relative to the total, so total emissions and hence any damage that they and otherssufferwill be unaffected bywhatever consumption choice theymake. In this context consumerbehaviour and the optimal environmental tax are independent of the degree of altruism. Forbehaviour to change, individuals need to make their decisions in a different way. We proposea new theory of moral behaviour whereby individuals recognise that they will be worse offby not acting in their own self-interest, and balance this cost off against the hypotheticalmoral value of adopting a Kantian form of behaviour, that is by calculating the consequencesof their action by asking what would happen if everyone else acted in the same way as theydid. We show that: (a) if individuals behave this way, then altruism matters and the greaterthe degree of altruism the more individuals cut back their consumption of a ‘dirty’ good;(b) nevertheless the optimal environmental tax is exactly the same as that emerging fromclassical analysis where individuals act in self-interested fashion.

Keywords Altruism · Climate change · Environmental economics · Environmental tax ·Externalities · Moral behaviour · Pro-social behaviour · Public goods

Marc Daube gratefully acknowledges financial support from the Economic and Social Research Council,grant number ES/J500136/1.

M. Daube · D. Ulph (B)School of Economics and Finance, University of St Andrews, St Andrews,Fife KY16 9AR, Scotland, UKe-mail: du1@st-andrews.ac.uk

M. Daubee-mail: mpl@st-andrews.ac.uk

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1 Introduction

In a recent paper assessing the challenges that policy-makers and society face in addressingclimate change, Galarraga and Markandya (2009) point out the key ethical and welfare con-siderations that need to be taken into account – in particular the intra-and inter-generationalimpact of the damage that climate change may bring.

While economists frequently consider these ethical considerations in terms of the formu-lation of the appropriate welfare objective for policy-makers to pursue, an equally importantissue is how far individuals themselves take these factors into account when deciding whatactions to take and what policies they are willing to support. This raises the important ques-tion of the extent to which policy actionmight be needed if individuals themselves are willingto alter their behaviour as they recognise the potential harm that their actions might cause.

As both Stern (2007) and Galarraga and Markandya (2009) point out, climate changerepresents one of the largest externalities that society has had to face, and, like all externalities,the fundamental need for policy intervention arises from free-riding behaviour—in this casenot just by individuals and companies but also by governments.

In the classical analysis of externalities, free-riding arises because individuals are purelyself-interested, and so perceive that, while they bear all the costs of changing their consump-tion behaviour, they may get only a very small gain in terms of the reduced damage that theythemselves will suffer. In the extreme case, individuals may calculate that their emissionsare so insignificant relative to the total, that total emissions and hence any damage that they(and others) might suffer will be unaffected by whatever consumption choices they make.1

In these circumstances individuals make their consumption choices ignoring any effect thesechoices have on climate change and the damage it will cause.2 The classic prescription is theintroduction of a Pigovian tax (equal to social marginal damage) so that individuals face thefull economic cost of their consumption decisions.

It is sometimes thought that if individuals are not self-interested, but instead are altruisticand so take account of the effect of their actions on others, this may overcome free-ridingbehaviour. However, as we will show, as long as individuals continue to believe that totalemissions are completely unaffected bywhatever they do, then howevermuch they care aboutothers, their behaviour will not change, and the optimal policy is to impose exactly the sametax as if individuals were self-interested.

For individual behaviour to change, individuals need to make their consumption decisionsin a different way. While there have been a number of theories of pro-social behaviour, thesetypically involve individuals obtaining some kind of utility gain from behaving morally. Inthis paper we propose a new theory of moral behaviour whereby individuals recognise thatthey will be worse off by not acting in their own self-interest, and balance this cost off againsta hypothetical moral value of adopting a Kantian form of behaviour, that is by calculatingthe consequences of their action by asking what would happen if everyone else acted in thesame way as they did. We show that

(i) Individuals behaving this way will adjust their behaviour to take account of the impactof their decision on themselves and others.

1 We will refer to this inability to influence the total level of the externality as ‘atomistic’ consumption.2 Echoes of such free-riding behaviour can be found in a paper by Longo et al. (2012) reporting on a studyconducted in the Basque Country on people’s willingness to pay for the ancillary benefits of climate changemitigation. They note that, as in many such studies, while many people reveal a positive willingness to pay,there is group of “protestors” who say they do not want to pay for these benefits, either because they do notthink the proposed policy actions will be effective, or because they feel that others should contribute.

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(ii) If individuals behave in this way, then altruism matters and the greater the degree ofaltruism the more individuals cut back their consumption of a ‘dirty’ good.

(iii) Nevertheless the optimal environmental tax is exactly the same as that emerging fromthe classical analysis where individuals are purely self-interested.

A key result of this paper is that the existence of altruistic and ‘moral’ behaviour doesnot change the socially optimal tax on an environmentally harmful good. Johansson (1997)previously modelled the socially optimal tax on an externality for different types altruismand compared it to the standard Pigovian tax level. Contrary to our results he finds thatdepending on the type of altruism analysed, the socially optimal tax on the externality canbe higher, lower, or equal to the Pigovian tax. However, Johansson (1997) uses a differentapproach to analysing the case where individual’s behaviour is driven by something otherthan maximising their utility (Genuine Altruism), and finds that the optimal tax is lower thanunder standard theory.3

The paper will proceed as follows. In Sect. 2 we conduct a brief discussion of the litera-ture on pro-social behaviour and altruism. Section 3 then develops the model, starting withstandard theory excluding any form of altruism in Sect. 3.1. This serves as counterfactualto the remaining analysis. We then proceed in Sect. 3.2 to layer on a type of Pure Altruismthat will be defined carefully in what follows. Section 3.3 then turns to the central element ofthis paper by developing the theory of moral behaviour. Finally, Sect. 4 will present a briefdiscussion of the model and the results.

2 Review of Literature

As described in the introduction, pro-social (and pro-environmental) behaviour is usuallyat odds with standard economic analysis, which predicts that in a non-cooperative setting,individuals onlymakenegligible contributions to public goods. For example,Andreoni (1988)shows that in large populations the share of individuals making contributions to a publicgood tends to zero as the free-riding effect dominates.4 However, when contributing to thepublic good also yields some utility benefit to the individual, voluntary contributions can beconsistent with standard economic models. Andreoni (1989, 1990) models the individual’sutility not just as a function of the consumption of the private and public goods, but alsoof the individual’s contribution to the public good itself. This is commonly referred to asthe ‘warm-glow’ effect and describes a form of Impure Altruism.5 ‘Warm-glow’ can also be

3 Johansson (1997) is not analysing a Kantian type of behaviour and therefore uses a different type of choicefunction that includes the individual’s and everybody else’s utility. He further assumes that all individuals areidentical in terms of their degree of altruism or morality.4 Also see Bergstrom et al. (1986).5 Andreoni’s development of warm-glow giving is based on the analysis of the provision of impure publicgoods by Cornes and Sandler (1984). The analysis of impure public goods also has importance in the areaof environmental policy. For example, Markandya and Rübbelke (2004) analyse ancillary benefits of climatepolicy and argue that policymakers should consider these more thoroughly. Further, Markandya and Rübbelke(2012) look at the under-provision of impure public technologies in an environmental context whileAltemeyer-Bartscher et al. (2014) take into account that climate policy is an impure public good in their analysis oftax-transfer schemes in relation to international public goods. However, Impure Altruism and impure publicgoods are not the same concept. Impure public good means that the good itself has some private characteristicsand this may impact individuals’ contribution to the public good. Whether a public good is a pure or impurepublic good depends on the characteristics of the good, and is independent of how the good is funded. However,Impure Altruism relates to the decision individuals make regarding the funding for the provision of the publicgood, and, in particular, to the relative weights they place on the benefits to themselves and to others in making

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interpreted as a self-image gain from contributing to the public good.6 While Andreonimakesno assumptions regarding the psychological cause of this ‘warm-glow’, various other authorshave developed more sophisticated models with regard to the underlying motivation. Thesemodels usually work on the premise that individuals derive intrinsic value from a self-imagedesire or social norms.Bénabou andTirole (2006), for example,model a “reputational payoff”(p. 1656) from contribution to a public good, which is also a function of the belief others haveregarding the type of consumer this individual is. In a model by Ellingsen and Johannesson(2008) the level of social approval depends on whether the individual himself approves ofthe person who approves him. Nyborg et al. (2006) also construct a model where individualsare motivated by a concern for self-image. However, this self-image is a function of the totalbenefit a ‘green’ good yields to the population, as well as their perception of what share of thepopulation is choosing to consume the ‘green’ option.7 This means the consumer’s intrinsicincentive to be pro-social increases as the share of the population acting that way increases.8

On the other hand, Brekke et al. (2003) develop a model where individuals are able to makea more sophisticated calculation of the “morally ideal effort” (p. 1971). This is achieved byevaluating the socially optimal contribution to a public good if they and everybody else wereto make the same choice. The individual then derives self-image value depending on howclose their contribution is to that socially optimal level, while trading off the self-image gainagainst the utility benefit from consumption.9

Essentially most of the contributions discussed above capture a form of Impure Altruismwhere, to some extent, the contribution itself matters to an individual’s utility. However,altruism is instead often viewed as a concern for the welfare of others.10 The two main typesof altruism that capture an individual’s concern for others’ welfare are Pure Altruism andPaternalistic Altruism. Pure Altruism uses the idea that an individual’s utility may to somedegree be a function of others’ utility, but not just a specific component of it. Applicationsof this type of altruism are often used with smaller settings, such as the family where onemight care about the welfare of specific individuals (for example Becker (1974, 1981)). Inlarge-scale contexts it can also be assumed that an individual cares for the total or average

Footnote 5 continuedthat decision. For example, a public good may of a pure nature (i.e. both non-excludable and non-rivalrous)and confer no private benefits of the type mentioned above. An altruistic individual will value the benefits thatthe provision of this good brings to others but may, in addition, derive some utility gain (warm-glow) fromknowing that they are taking an action (contributing) that gives benefits to others. The label ‘impure’ thereforerefers to the nature of utility derived from an altruistic action, but not to the properties of the public good theindividual is contributing to.6 Also note that Andreoni refers to the case of an individual who only cares about the total supply of the publicgood as Pure Altruism. However, although the total supply of a public good also affects others, we, as well asother literature on altruism, use the term Pure Altruism to refer to an individual’s direct concern for the utilityof others. We will provide a more detailed description of how we model Pure Altruism later in this section.7 To some extent this also captures the idea of a social norm or peer pressure.8 Because what matters in their model is the individual’s perception of what others do, Nyborg et al. (2006)further argue that policy makers may be able to influence this perception, for example through advertising.Also, a temporary tax on the environmentally harmful good could move the population to a permanent ‘green’equilibrium even when the tax is later removed.9 Another area of the literature where individuals may have utility gains from behaving in pro-environmentalways looks at individuals’ concern for relative consumption. An example relevant to the analysis of globalpublic goods such as climate protection is the work by Aronsson and Johansson-Stenman (2014), who lookat optimal provision of national and global public goods when individuals care about relative consumptionlevels.10 The literature on altruism is very rich and we will only make a superficial survey as relevant to this paper.For more detail, Fontaine (2008) provides a summary of the history of the concept of altruism in economics.

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welfare of all other individuals in the population (see Hammond 1987; Johansson 1997 forexamples).11 Paternalistic Altruism differs from Pure Altruism in that it does not assumethat an individual’s utility is a function of others’ utility as such, but a specific componentof that utility (see Archibald and Donaldson 1976). In an environmental context, this com-ponent may be the damage experienced by others from the environmentally harmful good.While Impure Altruism only takes into account the individual’s contribution to the exter-nality, Paternalistic Altruism means that the individual is affected by others’ experience ofthe externality, regardless of the individual’s contribution. All these types of altruism stillassume that individuals maximise their utility when acting pro-socially. Genuine Altruism asdefined by Kennett (1980), on the other hand, requires that individuals’ behaviour is drivenby some function other than maximising their utility. For example, the individual may makethe consumption choice by maximising a function consisting of their own utility and every-body else’s utility, but by doing so will incur a loss in utility compared to standard economicbehaviour.12 Since this implies a deviation from ‘rational’ behaviour driven by self-interesteconomists usually assume, it is the most drastic form of altruism.

Johansson (1997) models the socially optimal tax on an externality for all four types ofaltruism described above and compares it to the standard Pigovian tax level.13 He finds thatunder Pure Altruism the optimal level of tax is equal to the standard Pigovian level in largepopulations.14 However, with a form of Genuine Altruism where individuals maximise afunction of the weighted sum of their own utility and everybody else’s utility, Johansson(1997) finds that the optimal tax is lower than the Pigovian tax. The socially optimal level ofconsumption is unchanged from the standard level as this type of altruism does not affect it,but the individual will demand this lower level of consumption due to the functionmaximisedand therefore the requirement on the tax level is reduced. If the weight in the maximisationwere equal between the individual’s utility and all others’ utility, the tax rate would dropto zero.15 In his analysis Johansson (1997) recognises that Genuine Altruism is the mostcontroversial of all types of altruism as it contradicts mainstream economic theory. Yetthe traditional model has already for a long time drawn fundamental criticism. Sen (1977)describes why the economist prefers to assume the existence of a selfish being: “It is possibleto define a person’s interests in such a way that no matter what he does he can be seen to befurthering his own interests in every isolated act of choice.” (p. 322). Indeed it means thatevery action can be explained simply through the concept of revealed preferences. This savesthe economist from having to take a closer look at what constitutes preferences and utility, oras Sen (1977) puts it: “…a robust piece of evasion.” (p. 323). Sugden (1982) further arguesthat assuming utility-maximising behaviour in the traditional sense may be too constricting

11 Also see Nyborg and Rege (2003) for basic modelling approaches to public good provision including Pureand Impure Altruism.12 See Johansson (1997).13 Johansson (1997) uses a model of discrete, identical consumers, who choose between a ‘clean’ good anda ‘dirty’ good, which in turn causes the externality. The government imposes a tax on the dirty good, but taxrevenues are distributed back to the consumer.14 This result is driven by the assumption that the size of altruistic concern has to be small relative to theprivate consumption utility in order to maintain realistic proportionality of the utility function.15 Furthermore, for Paternalistic Altruism Johansson (1997) finds that the tax is higher than the Pigovian taxbecause, as individuals take into account others’ experience of the externality, the socially optimally level ofthe externality is reduced and therefore the optimal tax level increases. For the case of Impure Altruism, theoptimal tax is exactly equal to the Pigovian tax. Although the socially optimal level of consumption is lowerthan the standard level, this shift is exactly the amount that occurs due to the ‘warm glow’ from the individual’scontribution to the externality. Therefore, the optimal tax level does not need to be higher in order to achievethe socially optimal level of consumption.

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and different people might indeed maximise very different functions in order to determinetheir consumption choice.

The criticism presented here does not seek to suggest that the utility-maximising modelis without value, and the critical literature usually acknowledges the usefulness of the tradi-tional model, especially in market-exchange situations. But in the context of this paper it hasto be recognised that environmental issues are often subject to strong moral views.16 As Frey(1999) summarises, contrary to the utilitarian perspective, a moralist views the environmentwith unique value and believes that it should be protected purely for ethical reasons and withlittle or no regard to any trade-offs. Furthermore, Arrow (1986) argues that rationality asthe economist defines it often only occurs through market exchange, rather than through theintrinsic motivation of an individual. However, as Shogren and Taylor (2008) point out, envi-ronmental resources are frequently not subject to the market exchange required for consistentchoices. Furthermore, we put forward that when individuals realise that the government isnot able to set the incentives correctly, they may also recognise that the result will be farfrom optimal for themselves and everybody else without a change in behaviour. This may,in turn, lead to moral motivation that requires a different type of model to explain. Along thelines of Harsanyi (1955), Sen (1977) develops the idea that people may have two preferencerelations working at the same time.17 Utility-maximising behaviour with some considerationfor the utility of others he labels as ‘sympathy’, while actions driven only by their moralvalue with no consideration of utility he calls ‘commitment’.18 The latter is very much inline with Kant’s concept of ‘duty’.19

Laffont (1975) develops the idea of a Kantian approach to behaviour where individualsconsider what would be optimal if they and everybody else were to make the same choice.20

However, Laffont (1975) assumes that individuals are identical, with all individuals applyingthis rule equally. In his model this implies that individuals will correctly anticipate thateverybody else will indeed behave the same way, meaning that ultimately individuals stillmaximise their personal utility. Our approach differs to that of Laffont (1975) in thatwemodelindividuals having no expectations regarding the behaviour of others and they assume thatall others continue to behave in the utility-maximising way. Individuals therefore recognisethat acting morally means they will suffer a loss of personal utility. The central aspect of ourapproach is that individuals assess the intrinsic ‘moral value’ of their action by comparingthe utility they actually get to the utility they would get if everyone else were to make thesame choice as this individual.21 Individuals then trade of this hypothetical ‘moral value’ ofthe action against the associated utility cost when making their consumption choice.

16 Also see Bergstrom (2009) for a discussion of the links between moral rules and utility.17 The model developed in this paper can also be thought of as capturing the idea of two different preferencesets to some extent. However, combining two preference sets into a conventional model usually assumes thatone supersedes the other or individuals follow certain rules (see Thaler and Shefrin 1981 for an example). Themodel we present in this paper assumes that individuals trade-off moral preferences against utility preferencesdepending on their propensity to act morally.18 Sen (1977) also points out that the resulting behaviour may well be the same as the utility-maximising one,but that this may not have been the individual’s motivation.19 White (2003) provides a good summary of the essentials of Kant’s philosophy as relevant to an economistand discusses linking it to the traditional model of economic behaviour.20 Such an approach (a version of which is also used in our model) is generally inspired by Kant’s Formulaof Universal Law (a version of the categorical imperative) which states: “Act only according to that maximwhereby you can at the same time will that it become a universal law.” (Kant 1875, p. 421).21 This type of ‘Kantian’ calculation is similar to the one used by Brekke et al. (2003), although they link themoral value of this Kantian behaviour to a concern for self-image instead.

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In addition to the modelling of ‘moral value’, we also consider that individuals may havealtruistic concern for others’ utility (Pure Altruism). In line with Hammond’s (1987) defini-tion, wemodel that peoplemay exhibit altruistic concern for the utility of all other individualsas a collective. Specifically, our model assumes that an individual’s utility function is the sumof their direct utility from consumption and the total utility of all other individuals weightedby the degree of altruistic concern.22 While Johansson (1997) also models this form of PureAltruism, we differ by explicitly modelling a continuum of individuals in order to capturethe atomistic nature of individuals’ consumption choice in the context of large-scale environ-mental problems such as climate change. Such an individual would recognise the atomisticnature of their choice and hence, when making their consumption decision, takes averageand total levels of consumption, welfare as well as damage from the externality as given. It isnoteworthy that both the discrete and continuous approaches are widely used in the literaturedepending on the issue to be addressed. Finally, by modelling a combination of two differenttypes of altruism, ‘Pure Altruism’ (the concern for others’ utility) and ‘Genuine Altruism’(the propensity to actmorally through non-utility-maximising behaviour), we capture the ideathat people may be concerned about the welfare of others but may also have some propensityto act morally despite their inability to influence the impact of the environmentally harmfulgood.

Of course a distinction between Kant’s categorical imperative and our model is that Kantsees moral duties as absolute that completely supersede any considerations of utility. Ourmodel, on the other hand, does not use such a binary approach, but allows the individual’spropensity to act morally to determine in how far they are driven by the moral value of theaction relative to the associated loss in utility. Only individuals with full propensity to actmorally will completely disregard their own utility and act in a fully Kantian fashion. Atthe same time, individuals with no propensity to act morally will not take into account themoral value at all and thus act in a standard utility-maximising way. The propensity to actmorally is assumed to be an exogenous parameter that is distributed across different types ofindividuals in the economy. Since we make no assumption regarding what this distributionmay look like, we do not argue that people necessarily have a certain propensity to act morallybut we simply evaluate the consequences for the socially optimal tax on an environmentallyharmful good if some people do act this way.

3 The Model

3.1 Standard Theory

We start with a population consisting of a continuum of potentially different types of indi-viduals. These types are indexed by k ∈ [0, 1], 0 ≤ k ≤ 1. The distribution is given by thedensity function

f (k) > 0, k ∈ [0, 1] , where∫ 1

0f (k)dk = 1.

Each individual has the same initial endowment of income y > 0 and chooses between a‘clean’ good x and a ‘dirty’ good z. The clean good is a numeraire good with a price of 1 andtherefore represents the expenditure on all other goods but z. Its consumption is assumed to

22 Although for simplicity reasonswe assume that the degree of altruistic concern is the same for all individualsin the population, it is possible to generalise the result to allow for varying degrees of altruism for differenttypes of individuals without affecting the main conclusions from our analysis.

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generate no externalities. On the other hand, the dirty good generates one unit of emissionsper unit consumed, which is a negative externality to all individuals. Further, let ζ(.) denotethe function that assigns to an individual of type k their chosen consumption of the dirtygood, ζ(k) ≥ 0, and let z denote the average consumption of the dirty good. The size of thepopulation is measured by M > 0 and therefore total emissions E are

E = Mz, where z =∫ 1

0ζ(k) f (k)dk. (1)

Each individual derives utility from the personal consumption of the two goods. Forsimplicity we assume that preferences over the two goods are the same across all types andas such all individuals have identical utility functions.23 Additionally, utility is assumed tobe linear in consumption of the clean good in order to avoid issues of income distribution.24

This means as long as consumers always consume a positive amount of the clean good,the marginal utility of income is constant and welfare losses that may arise are not due toinequality but inefficiencies.

Utility derived from the consumption of the two good takes the following form:

u(x, z, E) = x + φ(z) − D(E)

where φ′(z) > 0, φ′′(z) < 0; and ∀E > 0, D′(E) > 0, D′′(E) ≥ 0. (2)

The damage fromemissions experienced by individuals is captured by the damage functionD(E). It is a strictly increasing and convex function for all positive levels of emissions.Furthermore, φ(z) describes the private gross benefit gained from consumption of the dirtygood and is strictly increasing and strictly concave in z.

The dirty good is produced by a perfectly competitive industry operating with constantunit costs c > 0. At the same time, the government imposes an emissions tax t ≥ 0 on theconsumption of z. The tax revenue is redistributed to the individuals through a lump-sumtransfer σ that is identical for all individuals. Therefore the government budget constraint isdefined by

σ = t z. (3)

Using the definition of emissions provided in (1) and the government budget constraint, wecan now derive the utility from personal consumption and emissions as a function that onlydepends on the individual’s consumption level of the dirty good, and the average consumptionof the dirty good:

u(z; z, t) = (y + t z) − (c + t)z + φ(z) − D(Mz). (4)

In line with the idea of atomistic consumption, in all stages of the analysis we use thestandard Nash assumption that the individual always takes the consumption by everyone elseas given when making the choice over consumption of the dirty good. This means that theindividual treats average emissions as independent of z because their choice of consumptionof the dirty good has no influence on average and total emissions. Indeed, based on thedefinition of total emissions as shown in (1), even if every other individual of the same typeas this one were to change their consumption simultaneously, it would still not impact thelevel of average or total emissions.

23 Although individuals have identical utility functions, different types of individuals will later be defined bytheir propensity to act morally.24 Income distribution is of course an important element in the analysis of environmental externalities. How-ever, in order to isolate the effect of altruism and moral behaviour on individuals’ consumption choice, wehave kept issues of income distribution out of this analysis.

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Using this basic setup, the individual chooses z to maximise their direct personal utility asgiven by (4). Under standard utility-maximising behaviour the chosen level of consumptionof the dirty good can therefore be characterised by

φ′[z(t)] = c + t. (5)

As we would expect, the left hand side of (5) describes the marginal gross benefit ofconsumption of the dirty good and the right hand side describes the private marginal costof consumption. Further, as we would expect given the atomistic nature of the consumptionchoice in this model, the damage incurred from the dirty good is not a factor in determiningthe chosen consumption level under standard theory.

Given this we can determine that for any tax rate t and any dirty good assignment functionζ(.), social utility across all individuals in the population is

S(ζ, t) = M∫ 1

0u [ζ(k), z, t] f (k)dk, where z =

∫ 1

0ζ(k) f (k)dk. (6)

Since individuals have identical, and strictly concave utility functions, the socially optimalconsumption level requires that everyone consume the same amount of the dirty good. Thiscommon level, z, is defined as

z = ArgMaxz

S (ζ, t) = ArgMaxz

[y − cz + φ(z) − D(Mz)]. (7)

As we can see, the social planner takes account of the link between the taxes paid on thedirty good and the lump-sum transfer received by consumers through the government budgetconstraint. This means that the socially optimal level of consumption is independent of thetax rate t . In addition, the social planner also takes into account the connection between theconsumption of the dirty good and total emissions. As we would expect, this means that thesocial planner can fully internalise the externality. The socially optimal level of consumptionof the dirty good z is then implicitly defined by

φ′(z) = c + MD′(Mz), where z < z(0). (8)

This shows that, from a social planner’s perspective, the social marginal cost of consump-tion consists of the direct marginal cost of production of the dirty good, as well as the socialmarginal damage created by the emissions externality, MD′(Mz), but not the tax on the dirtygood since the revenues are entirely redistributed to the individuals.

From (5) and (8) it is also straightforward to see that the government can achieve thesocially optimal consumption level by setting the tax on the dirty good equal to the socialmarginal damage of consumption (the standard Pigovian tax). Denoting this optimal tax rateby t , it follows that

t = MD′(Mz). (9)

So far we have only described the basic model setup and laid out the results under standardtheory. These will serve as a counterfactual for the remaining analysis.

3.2 Pure Altruism

As discussed in the introduction, Pure Altruism in this model means that individuals mayput some weight on the total utility of all other individuals in the population. Individuals willtherefore not only maximise their own private utility from consumption, but the (weighted)sum of their own private utility and the total utility of all others. For simplicity wewill assume

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that the degree of altruistic concern does not vary across different types of individuals.25 Theweight given to the total utility of others is denoted α ≥ 0 for all k. Then the total welfare ofan individual who consumes an amount z of the dirty good is26

w (z; ζ, t, α) = U (z; z, t) + αS (ζ, t) , where z =∫ 1

0ζ(k) f (k)dk. (10)

Given the atomistic nature of consumption, the total utility of all other individuals in thepopulation is simply equal to the social utility as defined in (6). Furthermore, individualsstill treat the consumption of all other individuals as given when making their consumptionchoice over the dirty good. This means individuals treat the assignment function ζ(k), andhence the average consumption level z, as well as the level of social utility S(.), as given.Indeed this means that individuals do not just take as given the damage they themselves sufferfrom the externality, but also the damage that everyone else suffers.

It follows that, with atomistic consumption, if the individual chooses the level of con-sumption of the dirty good that maximises total individual welfare, then, independent of thelevel of altruistic concern, consumption will be the same as the level that maximises theirutility as characterised by (5).

Since we assumed a constant level of α for all types of individuals, we still have identicalpersonal welfare functions for all individuals. Using (10) it is then straightforward to derivethat, for any given tax rate t and assignment function ζ(.), the total welfare of all individuals,or social welfare, is given by

W (ζ, t, α) = (1 + αM) S (ζ, t). (11)

This shows that the level of altruistic concern across the population only scales up the totallevel of welfare, but the socially optimal level of consumption is still one in which everyoneconsumes the same amount of the dirty good as determined by standard theory. Consequentlythe level of z is still defined by (8) and the optimal tax inducing everyone to consume thesocially optimal level is still described by (9). This result leads us to the first proposition.

Proposition 1 In a world of atomistic consumption, with every individual choosing theirconsumption by maximising their utility, altruistic concern for the utility of others has noimpact on the optimal level of consumption for the individual, the socially optimal level ofconsumption or the socially optimal tax level.27

Proof By maximising individual welfare as shown in (10), it is straightforward to derive thatφ′(z) = c + t , which is the same as derived without altruism in (5). Similarly, maximisingthe social welfare function as shown in (11), we derive that φ′(z) = c + MD′(Mz), the samelevel as under standard theory in (8). Combining these two findings it is also evident thatt = MD′ (Mz

)induces everyone to consume the same socially optimal amount, the same as

shown under standard theory without altruism.

25 This assumption makes it more straightforward to isolate the key drivers of behaviour when we developthe model of moral behaviour. It is, however, possible to allow the degree of altruism to vary across differenttypes without altering the key results of this paper.26 We will refer to the utility that includes the effect of altruistic concern as ‘welfare’. This is simply done toseparate the direct type of utility from the altruistic type.27 Note that this result does depend on the functional form used for the individual’s welfare function describedin (10). However, this result can be generalised to other functional forms, for example the case where individ-ual’s welfare takes the form w (z; ζ, t, α) = U (z; z, t) [S (ζ, t)]α .

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So far we have established the results with and without altruistic concern for the utility ofothers based on standard utility-maximising behaviour. We will now turn to the key part ofthis paper and develop the theory of moral behaviour.

3.3 Moral Behaviour

We start by assuming that initially everyone consumes z(t), which is the chosen consumptionlevel consistent with standard theory as derived in Sect. 3.1. And since we want to investigatewhether moral behaviour can make up for a shortfall in government policy, we further beginwith the assumption that the tax on the dirty good is below the socially optimal level, i.e.t < t , and therefore we also have z(t) > z.

The model of moral behaviour developed here assumes that individuals recognise that ifthey deviate from the consumption level z(t), they will incur a loss in personal welfare. Thismeans that individuals still know that the rational choice for them and everyone else wouldbe to choose z(t) (given the atomistic nature of consumption). However, they may also bedriven by moral concerns for the environment and recognise that the overall outcome willbe far from optimal for themselves and everyone else as long as the government continuesto set the wrong tax. This may induce some individuals to act differently. Such an individualmay measure a hypothetical moral value of deviating from the standard consumption levelwithout expecting any personal benefit from this moral action.28

Ourmodelmeasures the hypotheticalmoral value of the choice through a type of ‘Kantian’calculation as discussed in Sect. 2. This means that an individual with some propensity toact morally will assess how much better off they and everyone else would be if they andeveryone else were to choose the same level of consumption, z.29 As already mentioned, theindividual recognises that deviating will entail a cost to personal welfare, but may balance offthis cost against themoral value, depending on their propensity to actmorally.We assume thatdifferent types of individuals may differ in their propensity to act morally. Some individualsmay only be concerned with the moral value of their action and not take any account of theloss of personal welfare they will incur. Yet other individuals may give no weight to the moralvalue but fully take account of the personal welfare cost associated with deviating from z(t).In addition to the propensity to act morally, the model recognises that individuals may stillexhibit altruistic concern for others’ utility as modelled in the previous section. The previousresults have shown that altruistic concern does not have any influence on the consumptionchoice under utility-maximising behaviour so the question arises whether this changes whenindividuals have some propensity to act morally.

The first step is to quantify the level of welfare loss associated with deviating from theinitial consumption level. Let ζ(t) be the assignment function that assigns everyone the initiallevel of consumption z(t). Therefore the average consumption of the dirty good is also z(t).For an individual of type kwho gives altruistic weightα ≥ 0 to the utility of other individuals,this gives an initial welfare level of

w (z(t); ζ(t), t, α) = (1 + αM)[y − cz(t) + φ (z(t)) − D (Mz(t))

]. (12)

28 It is crucial to emphasize that moral value does not mean the individual derives any benefit (or utility) fromthe moral action.29 This is of course a simplification of Kant’s Formula of Universal Law. For the purposes of this analysis,and in line with other literature using a Kantian approach as discussed in Sect. 2, we translate the categoricalimperative in the sense that a Kantian calculation asks what would be optimal if everyone acted the same way(also see Laffont (1975); Brekke et al. (2003)).

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However, if the individual chooses a different level of consumption such that z ≤ z ≤ z(t),but everyone else carries on consuming z(t), this generates the following level of welfare forthe individual:

w (z; ζ(t), t, α) = U (z; ζ(t), t) + αM[y − cz(t) + φ (z(t)) − D (Mz(t))

]. (13)

Combining (12) and (13) leads us to the welfare cost of choosing a different level ofconsumption of the dirty good, z, as opposed to the initial level, z(t):

C(z; z(t), t) = w(z(t); ζ(t), t, α) − w(z; ζ(t), t, α)

= [φ (z(t)) − (c + t) z(t)

] − [φ (z) − (c + t) z] . (14)

It is noteworthy that in the calculation of the welfare cost everything that depends on whatthe other individuals do, and therefore anything associated with the level of altruistic concern,has cancelled out. In addition, since an individual’s choice has no impact on the total level ofemissions, the damage function has also cancelled out. The welfare cost is purely driven bythe difference in the private benefit and cost elements of the dirty good. Were the individualto minimise this cost they would choose φ′(z) = c + t and then we would be back at thestandard level of consumption where z = z(t). Intuitively, in order to minimise the cost ofdeviating from the initial consumption level, one would not deviate at all.

The next step is to derive a measurement of the hypothetical moral value of choosinga different level of consumption. As already mentioned, this moral value is assessed byevaluating the welfare the individual would obtain if they and everyone else were to choosethat same level of consumption. For an individual who places an altruistic weight α ≥ 0 onthe welfare of all other individuals this would yield the following level of welfare:

w(z, ζ K (z); t, α) = (1 + αM)[y − cz + φ(z) − D(Mz)], (15)

where ζ K (z) is the ‘Kantian’ assignment function that assigns everyone else the same levelof consumption of the dirty good as that chosen by the individual.

There are two factors the individual will incorporate when making this calculation. First,the individual sees that if they and everyone else choose the same level of z, then the lump-sumtransfer to the individual from the government tax revenues will equal the tax paid on the dirtygood, rendering the tax rate irrelevant for the level of welfare obtained. Second, the individualtakes account of the impact the choice of z has on total emissions and therefore the damageassociated with it. Since it is a specific calculation of the level of welfare if everyone were tochoose the same level of the dirty good, the individual effectively makes the same calculationa social planner would make. This means that the individual does not just evaluate the moralvalue for themselves, but also the benefit to everyone else in the population. Therefore, themoral value of choosing a level of consumption, z, as opposed to the initial level, z(t), is

B (z; z(t), t, α) = w(z, ζ K (z) ; t, α) − w (z(t); ζ(t), t, α)

= (1 + αM){[y − cz + φ (z) − D (Mz)]

− [y − cz(t) + φ (z(t)) − D (Mz(t))

] }. (16)

From here it is easy to see that were an individual to simply maximise the hypotheti-cal moral value, the individual would choose the socially optimum level of consumption zregardless of their level of altruistic concern for the utility of others.

We can now put together the moral value and welfare cost of deviating from the initiallevel by assuming an individual will make the consumption choice putting some weight onthe moral value of deviating and balancing this off against the associated loss in personal

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Moral Behaviour, Altruism and Environmental Policy 517

Fig. 1 Consumption choice for individuals with some propensity to act morally

welfare. Let this propensity to act morally be measured by μ. For simplicity we assume thatindividuals will choose their consumption by maximising the weighted difference betweenthe moral value and the associated personal welfare cost:

μB − (1 − μ)C, 0 ≤ μ ≤ 1. (17)

Substituting (14) and (16) into (17), we see that for an individual with 0 ≤ μ ≤ 1,consumption of the dirty good will be chosen to

MAXz

μ(1 + αM)[y − cz + φ(z) − D(Mz)] + (1 − μ)[φ(z) − (c + t)z]. (18)

At this point it is noteworthy that, due to the linear nature of the choice function, the initiallevel of consumption z(t) is irrelevant to the consumption choice and could indeed be at anylevel.

Now, if we let

k = μ(1 + αM)

1 + μαM, 0 ≤ k ≤ 1, (19)

then it is straightforward to derive from (18) that the individual’s consumption choice can becharacterised by

φ′(z) = c + [kMD′(Mz) + (1 − k)t]. (20)

The parameter k is a combined parameter capturing both the individual’s propensity toact morally μ, and the level of altruistic concern for others’ utility α. This parameter canbe thought of as the overall level of ‘virtue’ individuals may exhibit, where 0 ≤ k ≤ 1.Examining (20), we see that if k = 1 the individual will choose a level of consumptionequal to the socially optimal level z = z = c + MD′(Mz). On the other hand, if k = 0,the individual will choose a consumption level of the dirty good equal to the conventionalchoice, z = z(t) = c + t . Of course the level of k can be anywhere between 0 and 1 and thelevel of z will vary accordingly between z(t) and z. Figure 1 illustrates the potential level ofconsumption for an individual with a value of k such that 0 < k < 1.

Next, let us take a closer look at the determinants of k. Suppose the individual has noaltruistic concern for others’ utility (α = 0). Then it follows that k = μ. This means that foran individual with no altruistic concern, behaviour only depends on the their propensity toact morally. However, if μ = 1, the individual will still cut down consumption of the dirtygood to z regardless of the level of α. Indeed we find that even if α = 0, an individual with

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μ > 0 will choose a lower consumption level of the dirty good relative to the standard level.It follows that altruistic concern for others’ utility is not a necessary component of this typeof behaviour.

Now suppose that the individual has no propensity to act morally (μ = 0). Then, it isstraightforward to see that k = 0 regardless of the value of α. Effectively, if μ = 0, we areback to the case where people choose consumption of dirty good bymaximising their welfarefunction which means that individuals will choose z(t) regardless of their level of altruisticconcern. Using these insights, we can set out the next proposition.

Proposition 2 Altruistic concern for others’ utility is neither necessary nor sufficient toinduce people to cut back consumption of the dirty good, but a propensity to act morally isboth necessary and sufficient.

Proof From (20) we know that z is a decreasing function of k for any t < t . From (19) wecan further determine that if μ = 1 → k = 1, if μ = 0 → k = 0, and ∂k

∂μ= 1+αM

(1+μαM)2> 0

for any value of α. Therefore α is neither necessary nor sufficient, but μ is both necessaryand sufficient to induce a decrease in z.

However, let us now look at the case where individuals have some, but not full propensityto act morally (0 < μ < 1). Then k is an increasing function of α. This means that thelevel of altruistic concern can affect the consumption choice even though people recognisethat their consumption of the dirty good has no effect on total emissions and anybody else’swelfare. This is because, in calculating the hypothetical moral value of the action, people takeinto account their level of altruistic concern for others’ utility and therefore the impact theirchoice will have on everybody else’s utility, but the associated utility cost of the consumptionchoice is independent of the level of altruistic concern. Yet we should also note that, even ifα = 1, as long as μ < 1, an individual will never cut down consumption of the dirty goodall the way to z. This leads us to the next proposition:

Proposition 3 If individuals have some, but not full propensity to act morally, an individualwith a higher level of altruistic concern for others will reduce consumption of the dirty goodif the government sets the tax on the dirty good too low, but never all the way to the sociallyoptimal level.

Proof From (19) we can derive that ∂k∂α

= μM(1−μ)

(1+μαM)2> 0 for any 0 < μ < 1. Therefore k is

an increasing function of α. Furthermore, we know from (20) that z is a decreasing functionof k for any t < t . Therefore an increase in α will lead to a reduction in the consumption ofthe dirty good for any 0 < μ < 1. However, to achieve z = z, we require k = 1. As per thedefinition of k in (19), this is only the case when μ = 1 and therefore z = z can never beachieved for any 0 < μ < 1 regardless of the value of α.

Next, suppose that the individual has some level of altruistic concern and some propensityto act morally (i.e. α > 0, and μ > 0). Then we can see that k is also an increasing functionof the size of the population, M . It shows that the larger the population of people affected,the more people will cut back their consumption of the dirty good. The size of the populationdoes not just influence the level of k though. Taking a closer look at (20) it is easy to seethat for individuals with some propensity to act morally (i.e. k > 0), there is another channelthrough which an increase in M will cause individuals to cut back their consumption ofthe dirty good. An increase in M increases the social marginal damage of consumption

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Moral Behaviour, Altruism and Environmental Policy 519

and therefore reduces the socially optimal level of consumption z.30 The population size Mimpacts the social marginal damage because, (a) it increases the number of people affected,and (b) it increases the total level of emissions which leads to increasing marginal damagesince damage is convex in z (ie D′′ > 0). We can now state the following general proposition.

Proposition 4 If the government fails to set the tax that would be optimal given the usualeconomic behaviour and the usual conception as to what constitutes welfare, then, to theextent that individuals have some propensity to act morally, private action will to someextent compensate for the lack of government action and drive consumption of the dirty gooddown towards the optimal level.

Proof For any 0 < μ ≤ 1 we have 0 < k ≤ 1 as per the definition of k in (19). Usingthis and comparing (20) with (5) and (8), it is straightforward to see that we must haveφ′ (z

) ≥ φ′ (z) > φ′[z(t)] and therefore we also know that z ≤ z < z(t).

We further know that although people may behave according to a different set of rules,individuals’ welfare is still determined by the altruistic welfare function as defined in (10).The government recognises this and therefore still uses the same social welfare function givenin (11) to determine the socially optimal allocation of welfare. Similarly, the social utilityfunction S(.) is also still the same as described in (6). It is then straightforward to see that thesocially optimal tax level for the government is still the standard Pigovian tax rate t , the samethat would be optimal if the population had no propensity to act morally (i.e. μ = 0 for alltypes). Indeed, by examining (20) while plugging in the Pigovian tax as shown in (9), we caneasily determine that each individual will choose consumption level z regardless of the levelof k. This means with a tax rate equal to t we can still achieve the first-best solution whereeveryone consumes the same amount of the dirty good and the damage is fully internalised.This leads us to the final proposition.

Proposition 5 Although individuals may to some extent compensate for the government’sfailure to set the optimal tax, this does not imply that the government should not set theoptimal tax.

Proof From (20) we can derive that by increasing t to t = MD′ (Mz)everyone will consume

z as characterised by (8). This raises social welfare because (a) aggregate consumption ofthe dirty good is socially optimal and (b) consumption is equalised across consumers.

Initially we assumed that the government set the tax on the dirty good below the optimallevel (t < t). Now suppose that the government actually sets the tax rate too high, so t > tand therefore z(t) < z. Because the initial level of consumption is now lower than the sociallyoptimal level, an individual with some propensity to act morally will actually increase theirconsumption of the dirty good in order to bring it closer to the socially optimal level. Thebenchmark for an individual with some propensity to act morally is always the sociallyoptimal level of consumption and depending on the weight they give to the moral value, theywill choose a consumption level of the dirty good that moves closer to z. This point illustratesthat the propensity to actmorally does not necessarily imply a reduction in the consumption ofan environmentally harmful good. Rather, an individual with some propensity to act morallywill change consumption in order to get closer to the social optimum in the absence of thecorrect tax on the dirty good.31

30 This impact ofM on the socially optimal level of consumption is of course not an exclusive feature of moralbehaviour as modelled here, but can also be observed in the characterisation of the socially optimal level ofconsumption as shown in (8).31 Buchholz et al. (2012) also analyse a case of public good provision where the subsidy may be too high.

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4 Discussion

The aim of this paper was to develop an alternative model of moral behaviour and altruismin an environmental context and evaluate what implications such behaviour may have forenvironmental policy. We have shown that when people have some propensity to act morallythey will cut back consumption of an environmentally harmful good. At the same time,altruistic concern for the utility of others can contribute to the amount that individuals cutconsumption, but only if they also have some propensity to act morally. The optimal tax onthe dirty good remains the same as under standard theory and the first-best solution can beachieved. A key reason for this is that, even though some individuals may cut consumptiontowards to socially optimal level for moral reasons, we are still only dealing with marketfailure, which the Pigovian tax can correct for all individuals. However, this result hinges onindividuals correctly making the (sophisticated) calculation of themoral value when acting inthis genuinely altruistic way.Wementioned earlier that the individual recognises both the linkto the government budget constraint as well as the impact on total emissions when makingthis calculation. Suppose instead that the individual fails to take account of the connectionto the government budget constraint. It is then straightforward to show that an individualwith full propensity to act morally (μ = 1 → k = 1) will actually overcompensate andconsume less than the socially optimal level. At the same time, a tax at the Pigovian levelmeans that every individual with some propensity to act morally (k > 0) will consume lessthan the socially optimal level. Indeed, we are no longer able to find a tax rate that inducesthe first-best solution where everyone consumes the same amount of the dirty good. This isbecause we are now dealing with a behavioural failure as well as a market failure, whichcannot both be corrected with a single instrument. We would need a separate mechanism tocorrect the behavioural failure.32

Another key assumption in our model is that the propensity to act morally for each typeof individual is a given and static parameter. There are two questions that develop from thisobservation. First, where does the propensity to act morally come from?33 And second, canthe propensity to act morally be influenced by extrinsic incentives on the dirty good? Thelatter addresses whether the propensity to act morally can be crowded-in or crowded-out byextrinsic incentives. Crowding of intrinsic motivation has received a lot of attention in theliterature on pro-social behaviour due to its potential policy relevance.34 Extensions to ourpaper could investigate how the model can be adapted to give further insights on this issue.

Open Access This article is distributed under the terms of the Creative Commons Attribution License whichpermits any use, distribution, and reproduction in any medium, provided the original author(s) and the sourceare credited.

32 See Shogren and Taylor (2008) for a discussion on the existence of both market and behavioural failuresin an environmental economics context.33 This question is researched in a number of disciplines including psychology, sociology, neuroscience andevolutionary biology (see for example Heinrichs et al. 2013 for a variety of contributions on moral motivationfrom different fields of research). Extensions to this paper could make more detailed links between the insightsfrom those disciplines and the model developed in this paper.34 For example Frey (1997, 1999), Bénabou and Tirole (2006), Nyborg and Rege (2003), Nyborg et al. (2006)and Brekke et al. (2003) among others.

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